The propagation of light through materials with periodically modulated gain can present different effects that are analyzed in the paper. The characterization of these gain/loss metamaterials (GLM) with a two-dimensional modulation predicts the mode locked states and effects like non diffractive propagation of beams, superlaminar light propagation regimes and superdiffusion due to angular gain dependence. The last allows the management of amplification and spatial frequency filtering altogether, obtaining amplified, cleaned and focalized beams at the output of these kind of gain modulated materials. The characterization is obtained from the full Maxwell equations using the plane wave expansion (PWE) method, propagation through a given direction is simulated considering beam propagation in the paraxial approximation.